The former head of Brighton College has criticised state schools for their remorseless drive for exam success.
Sir Anthony, 62, said that they also had a grounding in soft skills such as creativity, empathy, grit, honesty, resilience and teamwork.
These were vital for success in the 21st century world of work, he told the Tatler Schools Live conference in Knighstbridge.
He said that the state sector had much to learn from independent schools. And he believed that the current Education Secretary Nicky Morgan was the first to appreciate the need for both academic rigour and the need to teach character and soft skills.
Sir Anthony was head of Brighton College from 1997 to 2005 when he left for another public school, Wellington. He took up his post at Buckingham University this year.
He has been a long-time advocate of teaching pupils to take care of their happiness and well-being.
Exam results did, however, improve markedly during his time at both Brighton College and Wellington.
Sir Anthony said: “Independent schools are taking the lead nationally in preparing students for the jobs required for the 21st century.
“As a Harvard study showed again last month, 21st century employers need much more than the skills developed in exams.
“They also need what are patronisingly called the ‘soft’ skills, ie, those that cannot be replicated by computers, which are fast taking over, not just manual but professional jobs also.
“These are skills of creativity, teamwork, empathy, grit, resilience and honesty.
“The remorseless drive in state schools for exam success is no longer fit for purpose.
“Students certainly need to be skilful at maths, science, languages and humanities. But they also need those skills that computers cannot replicate.
“Nicky Morgan is the first Secretary of State fully to appreciate that schools can excel at academic rigour and at teaching character, wellbeing and the soft skills that the 21st century economy and society require.
“The reason why alumni from independent schools are so dominant across society is not just because of the excellent exam results they receive but precisely because of the grounding in the soft skills.
“Though the best state sector (schools) manage to teach both for exams and for soft skills, the state sector overall has much to learn from the success of the British independent school model.
“I am expressly not critical of state schools themselves. They are the victim of forces that compel them to focus on a narrow range of exam teaching and subjects at the cost of broader education in the arts, character, sports and the social and work skills that employers increasingly want in the 21st century.
“Some state schools manage to do exams well and offer this breadth of education but it is much, much harder for them than independent schools.”